





from math import sqrt

def     a_       (					lowerCAmelCase_ :     int      ):
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ) and (
       number >= 0
   ), "'number' must been an int and positive"

   __lowerCAmelCase				      =      True

   # 0 and 1 are none primes.
   if number <= 1:
      __lowerCAmelCase				      =      False

   for divisor in range(2,      int(round(sqrt(lowerCAmelCase_      )      )      ) + 1      ):
      # if 'number' divisible by 'divisor' then sets 'status'
      # of false and break up the loop.
      if number % divisor == 0:
         __lowerCAmelCase				      =      False
         break

    # precondition
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ), "'status' must been from type bool"

   return status

def     a_       (					lowerCAmelCase_ :     int      ):
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ) and (n > 2), "'N' must been an int and > 2"

   # beginList: contains all natural numbers from 2 up to N
   __lowerCAmelCase				      =      list(range(2,      n + 1      )      )

   __lowerCAmelCase				      =      []  # this list will be returns.

   # actual sieve of erathostenes
   for i in range(len(lowerCAmelCase_      )      ):
      for j in range(i + 1,      len(lowerCAmelCase_      )      ):
         if (begin_list[i] != 0) and (begin_list[j] % begin_list[i] == 0):
            __lowerCAmelCase				      =      0

    # filters actual prime numbers.
   __lowerCAmelCase				      =      [x for x in begin_list if x != 0]

   # precondition
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ), "'ans' must been from type list"

   return ans

def     a_       (					lowerCAmelCase_ :     int      ):
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ) and (n > 2), "'N' must been an int and > 2"

   __lowerCAmelCase				      =      []

   # iterates over all numbers between 2 up to N+1
   # if a number is prime then appends to list 'ans'
   for number in range(2,      n + 1      ):
      if is_prime(lowerCAmelCase_      ):
         ans.append(lowerCAmelCase_      )

    # precondition
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ), "'ans' must been from type list"

   return ans

def     a_       (					lowerCAmelCase_ :     Tuple      ):
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ) and number >= 0, "'number' must been an int and >= 0"

   __lowerCAmelCase				      =      []  # this list will be returns of the function.

   # potential prime number factors.

   __lowerCAmelCase				      =      2

   __lowerCAmelCase				      =      number

   if number == 0 or number == 1:
      ans.append(lowerCAmelCase_      )

   # if 'number' not prime then builds the prime factorization of 'number'
   elif not is_prime(lowerCAmelCase_      ):
      while quotient != 1:
         if is_prime(lowerCAmelCase_      ) and (quotient % factor == 0):
            ans.append(lowerCAmelCase_      )
            quotient /= factor
         else:
            factor += 1

   else:
      ans.append(lowerCAmelCase_      )

   # precondition
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ), "'ans' must been from type list"

   return ans

def     a_       (					lowerCAmelCase_ :     Dict      ):
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ) and (
       number >= 0
   ), "'number' bust been an int and >= 0"

   __lowerCAmelCase				      =      0

   # prime factorization of 'number'
   __lowerCAmelCase				      =      prime_factorization(lowerCAmelCase_      )

   __lowerCAmelCase				      =      max(lowerCAmelCase_      )

   # precondition
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ), "'ans' must been from type int"

   return ans

def     a_       (					lowerCAmelCase_ :     Tuple      ):
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ) and (
       number >= 0
   ), "'number' bust been an int and >= 0"

   __lowerCAmelCase				      =      0

   # prime factorization of 'number'
   __lowerCAmelCase				      =      prime_factorization(lowerCAmelCase_      )

   __lowerCAmelCase				      =      min(lowerCAmelCase_      )

   # precondition
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ), "'ans' must been from type int"

   return ans

def     a_       (					lowerCAmelCase_ :     Optional[Any]      ):
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ), "'number' must been an int"
   assert isinstance(number % 2 == 0,      lowerCAmelCase_      ), "compare bust been from type bool"

   return number % 2 == 0

def     a_       (					lowerCAmelCase_ :     str      ):
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ), "'number' must been an int"
   assert isinstance(number % 2 != 0,      lowerCAmelCase_      ), "compare bust been from type bool"

   return number % 2 != 0

def     a_       (					lowerCAmelCase_ :     Any      ):
   assert (
       isinstance(lowerCAmelCase_,      lowerCAmelCase_      ) and (number > 2) and is_even(lowerCAmelCase_      )
   ), "'number' must been an int, even and > 2"

   __lowerCAmelCase				      =      []  # this list will returned

   # creates a list of prime numbers between 2 up to 'number'
   __lowerCAmelCase				      =      get_prime_numbers(lowerCAmelCase_      )
   __lowerCAmelCase				      =      len(lowerCAmelCase_      )

   # run variable for while-loops.
   __lowerCAmelCase				      =      0
   __lowerCAmelCase				      =      None

   # exit variable. for break up the loops
   __lowerCAmelCase				      =      True

   while i < len_pn and loop:
      __lowerCAmelCase				      =      i + 1

      while j < len_pn and loop:
         if prime_numbers[i] + prime_numbers[j] == number:
            __lowerCAmelCase				      =      False
            ans.append(prime_numbers[i]      )
            ans.append(prime_numbers[j]      )

         j += 1

      i += 1

   # precondition
   assert (
       isinstance(lowerCAmelCase_,      lowerCAmelCase_      )
       and (len(lowerCAmelCase_      ) == 2)
       and (ans[0] + ans[1] == number)
       and is_prime(ans[0]      )
       and is_prime(ans[1]      )
   ), "'ans' must contains two primes. And sum of elements must been eq 'number'"

   return ans

def     a_       (					lowerCAmelCase_ :     List[Any],      lowerCAmelCase_ :     int      ):
   assert (
       isinstance(lowerCAmelCase_,      lowerCAmelCase_      )
       and isinstance(lowerCAmelCase_,      lowerCAmelCase_      )
       and (numbera >= 0)
       and (numbera >= 0)
   ), "'number1' and 'number2' must been positive integer."

   __lowerCAmelCase				      =      0

   while numbera != 0:
      __lowerCAmelCase				      =      numbera % numbera
      __lowerCAmelCase				      =      numbera
      __lowerCAmelCase				      =      rest

   # precondition
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ) and (
       numbera >= 0
   ), "'number' must been from type int and positive"

   return numbera

def     a_       (					lowerCAmelCase_ :     str,      lowerCAmelCase_ :     List[Any]      ):
   assert (
       isinstance(lowerCAmelCase_,      lowerCAmelCase_      )
       and isinstance(lowerCAmelCase_,      lowerCAmelCase_      )
       and (numbera >= 1)
       and (numbera >= 1)
   ), "'number1' and 'number2' must been positive integer."

   __lowerCAmelCase				      =      1  # actual answer that will be return.

   # for kgV (x,1)
   if numbera > 1 and numbera > 1:
      # builds the prime factorization of 'number1' and 'number2'
      __lowerCAmelCase				      =      prime_factorization(lowerCAmelCase_      )
      __lowerCAmelCase				      =      prime_factorization(lowerCAmelCase_      )

   elif numbera == 1 or numbera == 1:
      __lowerCAmelCase				      =      []
      __lowerCAmelCase				      =      []
      __lowerCAmelCase				      =      max(lowerCAmelCase_,      lowerCAmelCase_      )

   __lowerCAmelCase				      =      0
   __lowerCAmelCase				      =      0

   __lowerCAmelCase				      =      []  # captured numbers int both 'primeFac1' and 'primeFac2'

   # iterates through primeFac1
   for n in prime_fac_a:
      if n not in done:
         if n in prime_fac_a:
            __lowerCAmelCase				      =      prime_fac_a.count(lowerCAmelCase_      )
            __lowerCAmelCase				      =      prime_fac_a.count(lowerCAmelCase_      )

            for _ in range(max(lowerCAmelCase_,      lowerCAmelCase_      )      ):
               ans *= n

         else:
            __lowerCAmelCase				      =      prime_fac_a.count(lowerCAmelCase_      )

            for _ in range(lowerCAmelCase_      ):
               ans *= n

         done.append(lowerCAmelCase_      )

    # iterates through primeFac2
   for n in prime_fac_a:
      if n not in done:
         __lowerCAmelCase				      =      prime_fac_a.count(lowerCAmelCase_      )

         for _ in range(lowerCAmelCase_      ):
            ans *= n

         done.append(lowerCAmelCase_      )

    # precondition
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ) and (
       ans >= 0
   ), "'ans' must been from type int and positive"

   return ans

def     a_       (					lowerCAmelCase_ :     str      ):
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ) and (n >= 0), "'number' must been a positive int"

   __lowerCAmelCase				      =      0
   __lowerCAmelCase				      =      2  # this variable holds the answer

   while index < n:
      index += 1

      ans += 1  # counts to the next number

      # if ans not prime then
      # runs to the next prime number.
      while not is_prime(lowerCAmelCase_      ):
         ans += 1

    # precondition
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ) and is_prime(
       lowerCAmelCase_      ), "'ans' must been a prime number and from type int"

   return ans

def     a_       (					lowerCAmelCase_ :     Dict,      lowerCAmelCase_ :     str      ):
   assert (
       is_prime(lowerCAmelCase_      ) and is_prime(lowerCAmelCase_      ) and (p_number_a < p_number_a)
   ), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

   __lowerCAmelCase				      =      p_number_a + 1  # jump to the next number

   __lowerCAmelCase				      =      []  # this list will be returns.

   # if number is not prime then
   # fetch the next prime number.
   while not is_prime(lowerCAmelCase_      ):
      number += 1

   while number < p_number_a:
      ans.append(lowerCAmelCase_      )

      number += 1

      # fetch the next prime number.
      while not is_prime(lowerCAmelCase_      ):
         number += 1

    # precondition
   assert (
       isinstance(lowerCAmelCase_,      lowerCAmelCase_      )
       and ans[0] != p_number_a
       and ans[len(lowerCAmelCase_      ) - 1] != p_number_a
   ), "'ans' must been a list without the arguments"

   # 'ans' contains not 'pNumber1' and 'pNumber2' !
   return ans

def     a_       (					lowerCAmelCase_ :     Optional[Any]      ):
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ) and (n >= 1), "'n' must been int and >= 1"

   __lowerCAmelCase				      =      []  # will be returned.

   for divisor in range(1,      n + 1      ):
      if n % divisor == 0:
         ans.append(lowerCAmelCase_      )

    # precondition
   assert ans[0] == 1 and ans[len(lowerCAmelCase_      ) - 1] == n, "Error in function getDivisiors(...)"

   return ans

def     a_       (					lowerCAmelCase_ :     int      ):
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ) and (
       number > 1
   ), "'number' must been an int and >= 1"

   __lowerCAmelCase				      =      get_divisors(lowerCAmelCase_      )

   # precondition
   assert (
       isinstance(lowerCAmelCase_,      lowerCAmelCase_      )
       and (divisors[0] == 1)
       and (divisors[len(lowerCAmelCase_      ) - 1] == number)
   ), "Error in help-function getDivisiors(...)"

   # summed all divisors up to 'number' (exclusive), hence [:-1]
   return sum(divisors[:-1]      ) == number

def     a_       (					lowerCAmelCase_ :     List[str],      lowerCAmelCase_ :     Any      ):
   assert (
       isinstance(lowerCAmelCase_,      lowerCAmelCase_      )
       and isinstance(lowerCAmelCase_,      lowerCAmelCase_      )
       and (denominator != 0)
   ), "The arguments must been from type int and 'denominator' != 0"

   # build the greatest common divisor of numerator and denominator.
   __lowerCAmelCase				      =      gcd(abs(lowerCAmelCase_      ),      abs(lowerCAmelCase_      )      )

   # precondition
   assert (
       isinstance(lowerCAmelCase_,      lowerCAmelCase_      )
       and (numerator % gcd_of_fraction == 0)
       and (denominator % gcd_of_fraction == 0)
   ), "Error in function gcd(...,...)"

   return (numerator // gcd_of_fraction, denominator // gcd_of_fraction)

def     a_       (					lowerCAmelCase_ :     Dict      ):
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ) and (n >= 0), "'n' must been a int and >= 0"

   __lowerCAmelCase				      =      1  # this will be return.

   for factor in range(1,      n + 1      ):
      ans *= factor

   return ans




def     a_       (					lowerCAmelCase_ :     Dict      ):
   assert isinstance(lowerCAmelCase_,      lowerCAmelCase_      ) and (n >= 0), "'n' must been an int and >= 0"

   __lowerCAmelCase				      =      0
   __lowerCAmelCase				      =      1
   __lowerCAmelCase				      =      1  # this will be return

   for _ in range(n - 1      ):
      __lowerCAmelCase				      =      ans
      ans += fiba
      __lowerCAmelCase				      =      tmp

   return ans







'''simple docstring'''


from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


UpperCAmelCase_					=   {
    "configuration_clap": [
        "CLAP_PRETRAINED_MODEL_ARCHIVE_LIST",
        "ClapAudioConfig",
        "ClapConfig",
        "ClapTextConfig",
    ],
    "processing_clap": ["ClapProcessor"],
}

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase_					=   [
      "CLAP_PRETRAINED_MODEL_ARCHIVE_LIST",
      "ClapModel",
      "ClapPreTrainedModel",
      "ClapTextModel",
      "ClapTextModelWithProjection",
      "ClapAudioModel",
      "ClapAudioModelWithProjection",
  ]
  UpperCAmelCase_					=   ["ClapFeatureExtractor"]

if TYPE_CHECKING:
  from .configuration_clap import (
      CLAP_PRETRAINED_MODEL_ARCHIVE_LIST,
      ClapAudioConfig,
      ClapConfig,
      ClapTextConfig,
  )
  from .processing_clap import ClapProcessor

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .feature_extraction_clap import ClapFeatureExtractor
    from .modeling_clap import (
        CLAP_PRETRAINED_MODEL_ARCHIVE_LIST,
        ClapAudioModel,
        ClapAudioModelWithProjection,
        ClapModel,
        ClapPreTrainedModel,
        ClapTextModel,
        ClapTextModelWithProjection,
    )


else:
  import sys

  UpperCAmelCase_					=   _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)



